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# Class Note for MATH 1310 at UH

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This 7 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 23 views.

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Date Created: 02/06/15

Direct Variation For two quantities x and y if there is a constant k such that ykx We say y varies directly as x Inverse Variation For two quantities x and y if there is a constant k such that We say y varies inversely as X Joint Variation For three quantities x y and Z if there is a constant k such that szxy We say Z varies jointly as y and x Section 33 7 L4 7 Page 1 of7 Example 13 Q varies directly as d If 1 5 then Q 35 Express the statement as a formula Use the given information to find the constant of proportionality Make sure you restate your formula with the constant value plugged in Section 33 7 L4 7 Page 2 of7 Example 14 y varies inversely as the square of x If x 5 then y 3 Express the statement as a formula Use the given information to find the constant of proportionality Make sure you restate your formula with the constant value plugged in Section 33 7 L4 7 Page 3 of7 Example 15 C varies directly With x and inversely With the square root ofw Ifx 4 and w 36 then C 10 a Write a formula to express the situation b Find the constant of proportionality c Find the value ofC when x 3 and w 25 Section 33 7 L4 7 Page 4 of7 Example 16 T varies jointly with x and the cube of z If x 2 and z3then T6 a Write a formula to express the situation b Find the constant of proportionality c Find the value of Twhen x 18 and z 2 Section 33 7 L4 7 Page 5 of7 Example 17 Natural gas provides 358 of US energy The volume of a gas varies inversely as the pressure and directly as the temperature Temperature must be measured in degrees Kelvin K a unit used in physics If a certain gas occupies a volume of 2 liters at 300K and a pressure of 18 newtons per square centimeter nd the volume at 340K and a pressure of 24 newtons per square centimeter Section 33 7 L4 7 Page 6 of7 Example 18 The bodymass index or BMI is used by physicians to assess a person s level of fatness The BMI varies directly as an individual s weight in pounds and inversely as the square of the individual s height in inches A person who weighs 118 pounds and is 64 inches tall has BMI 20 The BMI is rounded to the nearest whole number Find the BMI of a person who weighs 165 pounds with height 7 0 inches You can use a calculator on this one Section 33 7 L4 7 Page 7 of7

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